Number Sets and Real Numbers - Vocabulary

Vocabulary flashcards covering Real, Rational, and Irrational numbers, as well as related number sets (Integers, Whole, Natural), digits, and decimal types, based on the lecture notes.

Real numbers

All numbers that can be placed on a continuous number line, including both rational and irrational numbers.

Rational numbers

Numbers that can be expressed as the ratio of two integers (a/b with b ≠ 0); includes integers and terminating/repeating decimals.

Irrational numbers

Real numbers that cannot be written as a fraction; their decimals are nonterminating and nonrepeating (e.g., π, e, √2).

Integers

All whole numbers and their negatives, including zero: {…, -3, -2, -1, 0, 1, 2, 3, …}; no fractions.

Whole numbers

Nonnegative integers: {0, 1, 2, 3, …}.

Natural numbers

Positive integers used for counting: {1, 2, 3, …}.

Digits

The ten symbols 0 through 9 used to form numbers.

Decimal terminates

A decimal that ends after a finite number of digits (terminating decimal), e.g., 0.75.

Nonterminating decimal

A decimal that continues forever (does not terminate); may be repeating or nonrepeating.

Nonreal numbers

Numbers not on the real number line (e.g., the square root of a negative number).

Examples of irrational numbers

π, e, and √2 are classic examples; their decimals do not terminate and do not repeat.

Examples of rational numbers

Numbers like 4, 1.2, and -3 that can be written as a fraction a/b with integers a and b (b ≠ 0).

Common symbols for number sets

Z = integers; Q = rational numbers; R = real numbers; N = natural numbers; W = whole numbers; D = digits.

Set relationships (natural to real)

Natural ⊆ Whole ⊆ Integers ⊆ Rational ⊆ Real (and Real ⊆ Complex in broader math).